Properties, apparent molal

Helgeson, H. C. Kirkham D. H. and Flowers, G. C. Theoretical prediction of the thermod5mamic behavior of aqueous electrolytes at high pressure and temperatures IV. Calculation of activity coefficients, osmotic coefficients and apparent molal properties to 600°C and 5 kb, Am. J. Sci., 1981, 281, 1249-1516. 

The physical-chemical properties of natural waters are determined from the apparent molal properties () of the components of the mixture. The apparent molal property is related to the change that occurs when a salt is added to water. The apparent molal property is defined by... 

The Method of Apparent Molal Properties. We again consider a two-component system and show how the partial molal properties can be related to experimental data on apparent molal properties. The apparent molal property of component 2, G2, is defined by the equation... 

The partial molal enthalpy of the solute in a solution may not always be conveniently measured experimentally with the required precision. Usually, the apparent molal property for the solute is most used in connection with dilute solutions. For a solution of two components, the apparent molal enthalpy of the solute is... 

With most properties (enthalpies, volumes, heat capacities, etc.) the standard state is infinite dilution. It is sometimes possible to obtain directly the function near infinite dilution. For example, enthalpies of solution can be measured in solution where the final concentration is of the order of 10-3 molar. With properties such as volumes and heat capacities this is more difficult, and, to get standard values, it is usually necessary to measure apparent molal quantities 0y at various concentrations and extrapolate to infinite dilution (y° = Y°). Fortunately, it turns out that, at least with volumes and heat capacities, the transfer functions AYe (W — W + N) do not vary significantly with the electrolyte concentration as long as this concentration is relatively low (3). With most of the systems investigated, the transfer functions were calculated from apparent molal quantities at 0.1m and assumed to be equivalent to the standard values. 

The properties selected for evaluation include most of the thermodynamic properties which we normally evaluate in the course of our work in the data centers. They include enthalpies of formation, solution, and dilution Gibbs energies of formation and solution entropies of formation and solution heat capacities and equilibrium constants (solubility, ionization, etc) as well as activity and osmotic coefficients, relative apparent molal enthalpies and apparent molal heat capacities. 

Several studies of the physical properties of sulphates have been carried out these will not be treated in detail but are listed as follows a determination of the dissociation constants of some univalent sulphate ion-pairs,the electrostriction of ammonium sulphate, dielectric and n.m.r. investigations of phase transitions in lithium ammonium sulphate, the surface structure of barium sulphate crystals in aqueous solution, optical activity and the electro-optical effect in crystals of Cd2(NH4)2(S04)3, apparent molal volumes and heat capacities of Na2S04, K2SO4, and MgS04 in water, and densities, heats of fusion, and refractive indices of double sulphates of univalent metals. ... 

The next step is to perform a simultaneous regression of NaCl(aq) apparent molal volumes from 25-350 C. Over this wide range of temperature, however, and particularly above 300 C, standard-state properties based on the infinitely dilute reference state exhibit a very complex behavior (7,8), which is related to various peculiarities of the solvent. Thus in their representation of NaCl(aq) volumetric properties, Rogers and Pitzer (7) adopted a reference composition of a hydrated fused salt, NaCl IOH2O, to minimize the P and T dependence of the reference state volume and to adequately fit volumetric ta to 300°C and 1 kb. In this study the (supercooled) fused salt is used as the reference state. The equation for the apparent molal volume on this basis can be easily derived from that for the excess Gibbs energy of Pitzer and Simonson (, and is given by ... 

Apparent Molal and Standard and Relative Partial Molal Properties to 600"C and S kb". Am. J. Sci., v281, ppl249-1516 (1981)... 

Theoretical Prediction of the Thermodynamic Behavior of Aqueous Electrolytes at High Pressures and Temperatures IV. Calculation of Activity Coefficients, Osmotic Coefficients, and Apparent Molal and Standard Relative Partial Molal Properties to 600 °C and 5 kb... 

The apparent molal volumes and molal compressibilities of several monosaccharides, disaccharides and methyl pyranosides in dilute aqueous solution have been studied at 5, 15, and 25°C. The results were discussed in the light of solute-solvent interactions and a model for the hydration of galactose and lactose was proposed.The molal volumes of small carbohydrate molecules have been measured in an attempt at elucidating the relationship between molecular properties and sweetness. Molal volumes reflect fine differences in structure fe.q., axial or equatorial disposition of particular hydroxy groups) which are in turn related to differences in taste. In order to interpret differences in sweetness the viscosimetric constants and the heats of dilution of three monosaccharides, three disaccharides and the very sweet chlorinated sugar (21) have been determined, and their i.r. and Raman spectra have been recorded. The osmotic... 

In thermodynamics of solutions, the partial molal quantity and the apparent molal quantity for a component are usually defined [66]. In the properties of enthalpy, one deals with quantities which cannot be measured in an absolute sense. It is thus necessary to use a reference state from which to make the evaluations. Since the state of infinite dilution of the solute in the solvent is taken as reference, the specification of the composition of the solution by means of the molality m2 of the solute is consequently most convenient for the calculation of enthalpy. 

Millero FJ, Vinokurova F, Fernandez M, Hershey JP (1987) PVT properties of concentrated electrolytes. VI. The speed of sound and apparent molal compressibilities of sodium chloride, disodium sulfate, magnesium chloride and magnesium sulfate solutions from 0 to 100 °C. J Solut Chem 16 269-281... 

Helgeson HC, Kirkham DH, Flowers GC (1981) Theoretical prediction of the thermodynamic behavior of aqueous electrolytes at high pressures and temperatures. IV. Calculation of activity coefficients, osmotic coefficients, and apparent molal and standard and relative partial molal properties to 600 C and 5 KB. Am J Sci 281 1249-1516... 

The apparent molal volume belongs, from a formal point of view, to the same group of thermodynamic properties as the enthalpy of dilution. The expression for the concentration dependence of the apparent molal volume of a polyelectrolyte can be derived from the electrostatic free enthalpy in a way similar to that shown above. In the final expression, which is analogous to Equation (24), the derivative dA/dT is replaced by d2/dP. Recently, Skerjanc [28] has studied the apparent molal volume of solutions of polystyrenesulphonates and shown that the cell model is applicable within a wide concentration range. 

Mixtures of these surfactants with water result in solutions with unique properties that we want to consider. We will use the alkylpyridinium chlorides as examples. Figure 18.11 compares the osmotic coefficient 0, apparent relative molar enthalpy 4>L, apparent molar heat capacity Cp, and apparent molar volumes V as a function of molality for two alkylpyridinium chlorides in water.w19... 

The thermodynamic properties at T = 298.15 K shown in Figure 18.11 come from S. Causi, R. De Lisi, and S. Milioto, Thermodynamic properties of N-octyl-, N-decyl- and N-dodecylpyridinium chlorides in water , J. Solution Chem., 20, 1031-1058 (1991). Results at the other two temperatures are courtesy of K. Ballerat-Busserolles, C. Bizzo, L. Pezzimi, K. Sullivan, and E. M. Woolley, Apparent molar volumes and heat capacities at aqueous n-dodecyclpyridium chloride at molalities from 0.003 molkg-1 to 0.15 molkg-1, at temperatures from 283.15 K. to 393.15 K, and at the pressure 0.35 MPa , J. Chem. Thermodyn., 30, 971-983 (1998). 

Evidence for dimerization of the hydroxoaqua ion is based on the decrease of the number of chromium particles in reaction 10 and its increase in reaction 11. The number, v, of discrete chromium particles per diaqua ion should decrease from v = 1 to v = as the diaqua ion is titrated with 1 mol of OH" and then rise again to v = 1 as a second mole of OH" is added, v may be determined by measuring a colligative property of the solution. A most suitable method for ionic solutes is Three-Phase Vapor Tensiometry, TPVT i The three-phase solvent system consists of a saturated solution of an electrolyte in water, in equilibrium with the crystalline phase of that electrolyte and with water vapor. An isobaric temperature difference (AT)p is established when the pure solvent is equilibrated with a solution of a foreign solute in the same solvent, at constant pressure. The apparent number, Vm of free particles per formula of solute depends on the molality of the solute (m), the three-phase ebulioscopic constant Kg, and (AT)p... 

Enthalpy, Entropy, and Heat Capacity of Protein—Water Systems Below 0°C. A number of investigators have reported the apparent enthalpy of fusion as a function of temperature and composition for several hydrated proteins. MacKenzie and coworkers (10) determined absorption isotherms at low temperatures and found that 1) these absorption isotherms have essentially the same sigmoidal shapes as those observed above zero degrees 2) the magnitudes of the values for partial molal enthalpy and entropy increase as the content of unfrozen water decreases 3) the heat of fusion decreases as the content of unfrozen water decreases and 4) the heat capacity of the system increases as the content of unfrozen water increases. Taking these findings all together, the thermodynamic properties of unfrozen water are not very different from those of supercooled water at comparable temperatures. 

A single homogeneous phase such as an aqueous salt (say NaCl) solution has a large number of properties, such as temperature, density, NaCl molality, refractive index, heat capacity, absorption spectra, vapor pressure, conductivity, partial molar entropy of water, partial molar enthalpy of NaCl, ionization constant, osmotic coefficient, ionic strength, and so on. We know however that these properties are not all independent of one another. Most chemists know instinctively that a solution of NaCl in water will have all its properties fixed if temperature, pressure, and salt concentration are fixed. In other words, there are apparently three independent variables for this two-component system, or three variables which must be fixed before all variables are fixed. Furthermore, there seems to be no fundamental reason for singling out temperature, pressure, and salt concentration from the dozens of properties available, it s just more convenient any three would do. In saying this we have made the usual assumption that properties means intensive variables, or that the size of the system is irrelevant. If extensive variables are included, one extra variable is needed to fix all variables. This could be the system volume, or any other extensive parameter. 

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